KINETICS OF ION EXCHANGE ACCOMPANIED BY IRREVERSIBLE REACTION
ment by the latter mechanism, but the electron affinity of the molecule is most likely quite small and probably negative. Acknowledgments. The authors wish to express their gratitude to the Robert A. Welch Foundation for
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financial assistance, to Dr. Edward Chen for assistance in the experimental work and specifically for the data on 1-bromonaphthalene,to Miss Elsie Bryan for assistance in preparing the manuscript, and to Mr. Joe Steelhammer for the data on 1-chloronaphthalene.
The Kinetics of Ion Exchange Accompanied by Irreversible Reaction. I. Film Diffusion Controlled Neutralization of a Strong Acid Exchanger by Strong Bases
by R. A. Blickenstaff, J. D. Wagner, and J. S. Dranoff Department of Chemical Engineering, Northwestern University, Evanston, Illinois
(Received August 81, 1966)
An experimental study has been made of the neutralization of a strong-acid ion exchanger by strong-base solutions. The kinetic data obtained in a well-stirred batch reactor were found to be self-consistent and t o agree closely vith the model proposed by Helfferich for the conditions of film diffusion controlled reaction.
Introduction
Theory
The rates of ion exchange coupled with reaction have recently been explored in depth by Helfferich.’ He has developed the first detailed theoretical analysis of four different exchange-reaction systems and has presented a collection of rate laws for each system under conditions of intraparticle and external film diffusion rate control. HelfTerich’s analysis rests on the customary simplifying assumptions used in describing the ion-exchange process, including the coupled effects of concentration and electrical potential gradients on the diffusion of ionic species. The present work was undertaken to provide an experimental test of the first of the processes enumerated by Helfferich, the irreversible consumption by chemical reaction of counterions released from the solid exchanger during the exchange process. The results presented below indicate the analysis to be valid and furnish numerical values for the model parameters.
The basic reaction scheme under consideration is illustrated by -
H+
+ M + + OH-
M++ H ~ O
(I) where the barred quantities represent species in the resin phase. It is assumed that both the acid-form resin and the nelitralizing base are completely dissociated, while the water produced by the reaction is dissociated only to its usual slight extent. It is also assumed that the resin particles are uniform spheres, that the system remains isothermal, and that physical properties of the various species remain constant. The observable rate of the process which occurs when acid-form resin particles and basic solution are contacted in a batch reaction vessel will be controlled by diffusion of the various reactant species, ie., dif----f
(1) F.Helfferich, J. Phys. Chem., 69, 1178 (1965).
Volume 71, Number 6 May 1967
R. A. BLICKENSTAFF, J. D. WAGNER,AND J. S. DRANOFF
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fusion of base in the solution outside the particle and/or interdiffusion of Hf and M + ions within the particle. For the case at hand the rate-controlling process is taken to be diffusion of reacting species in the solution surrounding the particles. This, in effect, means that diffusion within the particle is fast enough to eliminate any concentration gradients in the resin phase. The external diffusion process may be conveniently idealized as taking place across a thin region of thickness 6 located a t the particlesolution interface, with no concentration gradients existing in the solution outside this film. In the case of neutralization, the only ionic species existing in the solution are the X4+ and OH- ions. These diffuse together across the film to the particle surface where the Mf ions enter the resin phase and are replaced in solution by H+ ions. The latter immediately react with the OH- ions of the solution to produce inert water. The conditions for film diffusion control of the over-all exchange rate are well known and comprise mainly small particle size and low solution concentrations. Following Helfferich,' one may derive rate laws for this process. It should be noted that these laws follow two related but distinct forms, dependent upon the relative ionic capacity of the solution and resin phases. Thus, when CV < CV, the fractional approach to equilibrium F(t) is given by
However, when CV >
for 0
5t5
t,, where
and F(t) = 1 for t 1 t,. It should be noted that for very small ratios of P tlo V ,eq 3 becomes linear, as shown in
